Abstract
Manifolds of visual motions lying in the high dimensional space are hard to comprehend and invisible. Facing this issue, we propose a novel method to visualize geometric transformations in images, where the projective transformations of SL(3) group are visualized based on multidimensional scaling(MDS). Based on the fact that the distance metric on SL(3) group doesn't have a closed form to compute, a novel method is created to solve this issue. As a result, we compute the corresponding coordinate-vectors in 3D state transition space that retains the given pattern of proximity in the high dimensional parameter space as much as possible for purpose of visualization. We test our methodology on synthetic images and real images respectively, getting convincing results in all cases.
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